We report the system design and predicted performance of the Florida IR Silicon immersion grating spectromeTer (FIRST). This new generation cryogenic IR spectrograph offers broad-band high resolution IR spectroscopy with R=72,000 at 1.4-1.8 μm and R=60,000 at 0.8-1.35 μm in a single exposure with a 2kx2k H2RG IR array. It is enabled by a compact design using an extremely high dispersion silicon immersion grating (SIG) and an R4 echelle with a 50 mm diameter pupil in combination with an Image Slicer. This instrument is operated in vacuum with temperature precisely controlled to reach long term stability for high precision radial velocity (RV) measurements of nearby stars, especially M dwarfs and young stars. The primary technical goal is to reach better than 4 m/s long term RV precision with J<9 M dwarfs within 30 min exposures. This instrument is scheduled to be commissioned at the Tennessee State University (TSU) 2-m Automatic Spectroscopic Telescope (AST) at Fairborn Observatory in spring 2013. FIRST can also be used for observing transiting planets, young stellar objects (YSOs), magnetic fields, binaries, brown dwarfs (BDs), ISM and stars. We plan to launch the FIRST NIR M dwarf planet survey in 2014 after FIRST is commissioned at the AST. This NIR M dwarf survey is the first large-scale NIR high precision Doppler survey dedicated to detecting and characterizing planets around 215 nearby M dwarfs with J< 10. Our primary science goal is to look for habitable Super-Earths around the late M dwarfs and also to identify transiting systems for follow-up observations with JWST to measure the planetary atmospheric compositions and study their habitability. Our secondary science goal is to detect and characterize a large number of planets around M dwarfs to understand the statistics of planet populations around these low mass stars and constrain planet formation and evolution models. Our survey baseline is expected to detect ~30 exoplanets, including 10 Super Earths, within 100 day periods. About half of the Super-Earths are in their habitable zones and one of them may be a transiting planet. The AST, with its robotic control and ease of switching between instruments (in seconds), enables great flexibility and efficiency, and enables an optimal strategy, in terms of schedule and cadence, for this NIR M dwarf planet survey.